Hooke's Law should be exponential.

[JCienfuegos]

I was just thinking, shouldn't hooke's law be represented with an exponential equation?
I am thinking that in class, the springs we use for the hooke's law experiment are small, but if they were very large, then the higher coils would be sustaining much more weight than the lower coils, and would thus be stretched more. I think this would lend itself more to an exponential model.

 

[NascentOxygen]

I guess the ideal model spring represented in Mr Hooke's law is one that is perfectly elastic and quite weightless.

Feel free to come up with a more accurate model for the ones in your lab. But be warned, you'll then have to look for some other plausible reason for your measurements not tallying so well with theory. Inaccurate modelling is always such a convenient excuse for general disagreement between theory and practice!

 

[Khashishi]

If you are familiar with Taylor series expansions, then you can understand that any system with a non-vanishing linear term in the expansion will behave close to linear for a perturbation from the equilibrium point sufficiently small. So, Hooke's law is trivial, but it works pretty well in practice.

 

[nasu]

I was just thinking, shouldn't hooke's law be represented with an exponential equation?
I am thinking that in class, the springs we use for the hooke's law experiment are small, but if they were very large, then the higher coils would be sustaining much more weight than the lower coils, and would thus be stretched more. I think this would lend itself more to an exponential model.

Hooke's law states that the strain (deformation) is proportional to the stress (tension, force). How will this be modified by the weight of the spring?
The deformation won't be uniform (as it is for weightless or horizontal spring on a table) but Hooke's law still applies as it is. In each piece of spring, the deformation will be proportional to the tension in that region. However the tension varies along the spring.
You can apply Hooke's law to find the deformation of an elastic bar or cable under its own weight.

Only if the deformation is too large Hooke's law will fail but this is not really related to the size of the spring or the existence of gravity. If you take a very small spring and you pull it hard enough, it won't get back to original size and shape. This is an example of non-elastic behavior.

 

[pmacias]

I appreciate your critical thinking and questioning of established theories. However, I must clarify that Hooke's Law is based on the principle of proportionality, which states that the force applied to a spring is directly proportional to the amount of stretch or compression it experiences. This is represented by a linear equation, F = kx, where F is the force, k is the spring constant, and x is the displacement.

While it is true that in larger springs, the higher coils may experience more weight and therefore be stretched more, this does not necessarily mean that Hooke's Law should be represented with an exponential equation. In fact, as long as the principle of proportionality holds true, the relationship between force and displacement will remain linear.

Furthermore, the use of smaller springs in the classroom setting is simply for practicality and ease of experimentation. Hooke's Law has been proven to hold true for a wide range of spring sizes and materials, and the linear equation has been extensively tested and validated through experiments.

In conclusion, Hooke's Law should remain represented with a linear equation, as it accurately describes the relationship between force and displacement in springs of all sizes. I encourage you to continue questioning and exploring scientific concepts, but always base your conclusions on solid evidence and scientific principles.